Assessing multiple beliefs according to one body of evidence — Why it may be necessary, and how we might do it correctly

Abstract

Dempster's rule of combination, the main inference mechanism of the Dempster-Shafer theory of belief functions [Shafer 76; Smets 88], requires that the belief functions to be combined must be "independent". This independence assumption is usually understood to be composed of two parts: (1) the uniqueness assumption, which states that each belief function to be combined is based on a unique body of evidence, and (2) the evidential independence (or distinctness) assumption, which states that we must be able to argue about the independence of all these different bodies of evidence. In this paper, we suggest that the uniqueness assumption is not necessary, and that it should be alright if we can come up with "independent specifications" of beliefs.